Introduction

Welcome to our comprehensive guide to solving the algebraic equation 2x2yy. This article is designed to help you understand how to manipulate and simplify algebraic expressions to find the value of (x). Let's break down the process step by step, ensuring that every step is clear and easily understandable.

1. Initial Expression

The given equation is:

(2x2y y)

Our goal is to find the value of (x). Let's start by simplifying this equation.

2. Simplifying the Equation

Step 1:

(2x2y y)

First, we can rewrite the left-hand side of the equation to make it clearer:

(4xy y)

Now, let's isolate (x) by dividing both sides of the equation by (4y):

(x frac{y}{4y})

By simplifying the fraction on the right-hand side, we get:

(x frac{1}{4})

This is our simplified result.

However, if the equation is given in the original form (2xy^2y), let's explore that version as well:

2. Simplifying the Original Equation

Given:

(2xy^2 y)

Step 1:

First, we can factor out (y) on the right-hand side:

(2xy^2 - y 0)

Step 2:

Factor (y) from both terms on the left-hand side:

(y(2xy - 1) 0)

Step 3:

This equation can be solved by setting each factor equal to zero:

0 (y) or (2xy - 1 0)

Case 1: (y 0)

Case 2: Solving for (x) in (2xy - 1 0):

(2xy 1)

(x frac{1}{2y})

This means that (x) is inversely proportional to (y).

3. Conclusion

So, depending on the form of the equation, the value of (x) can be either:

(x frac{1}{4}) or (x -0.5y).

It is crucial to understand the algebraic manipulations involved in solving equations. By mastering these steps, you can efficiently solve more complex algebraic equations in the future.

Keywords: algebraic equations, algebra simplification, solving equations